Explanation
For triangle XPY we have:
[tex]\begin{gathered} tan(30°)=\frac{22}{XY} \\ XY=\frac{22}{tan(30°)} \\ XY=\frac{22}{\frac{\sqrt{3}}{3}} \\ XY=\frac{66}{\sqrt{3}} \\ XY=\frac{66\sqrt{3}}{3} \\ XY=22\sqrt{3} \end{gathered}[/tex]
Then
[tex]XU=44\sqrt{3}[/tex]
For the triangle XYZ we have:
[tex]\begin{gathered} tan(60°)=\frac{ZY}{22\sqrt{3}} \\ ZY=tan(60°)22\sqrt{3} \\ ZY=\sqrt{3}*22*\sqrt{3} \\ ZY=3*22 \\ ZY=66 \end{gathered}[/tex]
Answer
[tex]XU=44\sqrt{3}\text{ cm}[/tex][tex]ZY=66\text{ cm}[/tex][tex]m\angle RPY=120°[/tex]
